Energy consumption of computing has found increasing prominence but the area still suffers from the lack of a consolidated formal theory. In this paper, a theory for the energy consumption of computing is structured as an axiomatic system. The work is pure theoretical, involving theorem proving and mathematical reasoning. It is also interdisciplinary, so that while it targets computing, it involves theoretical physics (thermodynamics and statistical mechanics) and information theory. The theory does not contradict existing theories in theoretical physics and conforms to them as indeed it adopts its axioms from them. Nevertheless, the theory leads to interesting and important conclusions that have not been discussed in previous work. Some of them are: (i) Landauer's principle is shown to be a provable theorem provided that a precondition, named macroscopic determinism, holds. (ii) It is proved that real randomness (not pseudo randomness) can be used in computing in conjunction with or as an alternative to reversibility to achieve more energy saving. (iii) The theory propounds the concept that computers that use real randomness may apparently challenge the second law of thermodynamics. These are computational counterpart to Maxwell's daemon in thermodynamics and hence are named daemon computers. (iv) It is proved that if we do not accept the existence of daemon computers (to conform to the second law of thermodynamics), another type of computers, named clairvoyant computers, must exist that can gain information about other physical systems through real randomness. This theorem probably provides a theoretical explanation for strange observations about real randomness made in the global consciousness project at Princeton University.

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守护计算机与透视计算机：计算能耗的纯理论观点

计算的能源消耗越来越突出，但该领域仍然缺乏统一的形式理论。在本文中，计算能耗的理论被构建为一个公理系统。这项工作是纯理论的，涉及定理证明和数学推理。它也是跨学科的，因此虽然它的目标是计算，但它涉及理论物理学（热力学和统计力学）和信息论。该理论与理论物理学中的现有理论并不矛盾，并且符合它们，因为它确实从它们中采用了公理。然而，该理论得出了以前工作中没有讨论过的有趣且重要的结论。其中一些是： (i) Landauer 原理被证明是一个可证明的定理，前提是一个前提条件，称为宏观决定论，成立。(ii) 已证明真实随机性（而非伪随机性）可与可逆性结合或替代可逆性用于计算，以实现更多节能。(iii) 该理论提出了一个概念，即使用真正随机性的计算机可能会明显挑战热力学第二定律。这些是热力学中麦克斯韦守护进程的计算对应物，因此被命名为守护进程计算机。(iv) 证明如果我们不接受守护计算机的存在（以符合热力学第二定律），则必须存在另一种计算机，称为千里眼计算机，它可以通过真正的随机性获得有关其他物理系统的信息.